The silver and copper crystals of an eutectic Ag‐Cu alloy (71.9 wt% Ag) get a fibre‐like shape by wire drawing after a high degree of deformation. The extremely thin silver and copper fibres attain a diameter of about 100 Å at a reduction of cross section η = 99.99%. Such in‐situ‐produced silver‐copper composite wires show extensive anomalies of the conduction phenomena due to the size effect. Especially, the interaction of the fibre interfaces with the conduction electrons causes an extraordinary decrease of the electrical conductivity. This anomalous change of the resistivity as function of the diameter of the silver and copper fibres can be explained by the free‐path theory of the conduction electrons. The mean free paths of the conduction electrons of silver and copper as well as their scattering factors were determined at different test temperatures. The measured values are in good agreement with the calculated ones, obtained by the strict theory.